In many consumer products and manufacturing machines, high-precision motion systems may be embedded. Examples of consumer products with high-precision motion systems are hard disk drives, optical drives, and tape drives. Examples of manufacturing machines with high-precision motion systems are scanning lithography stages, and pick and place robots.
A typical controller for a high-precision motion system consists of a feedback controller and a feedforward controller. The feedforward controller uses the knowledge on the positioning setpoint to generate a feedforward command in such a way that the open loop response (with the feedback controller inactive) of the motion system resembles the setpoint as closely as possible. Different types of feedforward control can be distinguished. In the next paragraphs, two methods are discussed in more detail: Low-order Feedforward Control and Iterative Learning Control.
Low-order feedforward control (LFC) is well known and widely spread in industry. A low-order feedforward controller often includes different parts. A first part may be related to the setpoint acceleration, to generate the part of the command that is inertia-related. A second part may be related to the setpoint velocity, to generate the part of the command that is damping-related or friction-related. In the most advanced implementations, a third part may be related to the setpoint snap (identical to the derivative of jerk), to generate the part of the command that is related to the elastic deformation of the motion system. Advantages of LFC are its simplicity, its ease of implementation, and its flexibility against variations in the motion profile to be realized. A disadvantage of LFC is the required effort and time spent in manually tuning the coefficients of the different feedforward parts. Another disadvantage of LFC is the fact that the feedforward controller may not adapt to variations, in particular slow variations, in the motion system, in which case the performance will degrade.
Iterative Learning Control (ILC) is a methodology, which updates the control signal for a repeating task iteratively in such a way that the difference between the desired and the actual behavior of the system-to-be-controlled vanishes. ILC has been successfully applied in several applications. However, the main strength of ILC is also its main weakness: for repeating tasks, excellent feedforward signals can be designed, whereas these feedforward signals are useless for motion profiles with different characteristics, such as maximum displacement, velocity, acceleration. Thus, ILC may be inflexible, or, in the best case, only partially flexible for different motion profiles. Another disadvantage of ILC is that it usually needs rather extensive on-line computing and the storage and update of lengthy feedforward tables. An advantage of ILC is its ability to adapt to slow variations in the motion system, for example to changes in the inertia of the system or in motor constants.
An example of an apparatus including several high-precision motion systems is a lithographic apparatus, which is described hereinafter.
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In a lithographic apparatus, high-precision motion systems may be found for performing the stepping and scanning operations.